1. groupadd wpsolve
2. usermod -a -G www-data wpsolve (-a = append, -G is group, so replace www-data with your other username here)
3. You can either chmod 777 or do 775 and change the wp-content group to wpsolve. Which would be like this: chown -R www-data:wpsolve /home/example_user/public/example.com/public/wp-content && chmod -R 775 /home/example_user/public/example.com/public/wp-content(where the -R flag causes recursive)
Though I'm not sure if that would be the best solution. Apache runs as user www-data, I believe PHP does as well with a LAMP stack, so you probably have uploaded the files as your normal user, so probably running this command would fix it as well:
chown -R www-data:www-data /home/example_user/public/example.com/public

Good luck
By the way, I believe the best way to do it is with PHP-FPM instead of the default one used by Apache. PHP-FPM you can set the user to the one you use for uploading files, and then you can simply let that user be the owner without running into permission issues.